"I think I've done it right, can you verify?

1) logx^2 = -10

x^2 = 10^-10

x = 100000"

log x^2 = -10

10^-10 = some number between 0 and 1.

In fact, x^2 = 1/10,000,000,000.

So x = sqrt(10^-10) = 1/100,000.

You need to invert your answer.

If 0 < x^2 < 1 then x < 1.